I read about the Carnot Cycle and Carnot engine where it was said that the work done by this engine is equal to the area enclosed in the PV diagram. I understood the proof and everything but I am not able to get an intuitive idea of how the system is doing work in a complete cycle? Clearly the gravitational potential energy of system does not increase because P and V after a complete cycle remains same so no mass changes its height after complete cycle. Can I connect a dynamo somewhere in some way and get electrical energy? How exactly does this engine do work and how can I obtain energy from it?

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    $\begingroup$ This image gives an example: physics.louisville.edu/cldavis/phys298/notes/… $\endgroup$ – Pieter Oct 27 '18 at 17:25
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    $\begingroup$ In a sense the question should be in the subjective (i.e. How would the work done by ... ) because—as far as I know—there simply aren't any practical designs that actually attempt to implement the Carnot cycle. All the changing of which reservoir the system is in contact with that appears in @Pieter's figure as moving the cylinder around is hard to arrange in a practical device. $\endgroup$ – dmckee Oct 27 '18 at 18:37

I agree with dmckee’s comment on Pieter’s figure, which is a typical depiction of the Carnot cycle operating on an ideal gas with a piston/cylinder being the “engine”. Not only is it hard to arrange the piston/cylinder moving around between thermal reservoirs, there is also the issue of adding and removing thermal insulation in going between the adiabatic and isothermal processes.

A theoretical application not involving the aforementioned limitations is in the application of the Carnot cycle as a two-phase steam power cycle alternative to the Rankine cycle. See the T-S diagram below. Here at least the output of the Carnot cycle is steam turbine work, which can be clearly visualized to generate electrical power.

However even in this application the Carnot cycle is not practical. To name a few, there are practical issues in designing an isentropic compressor to compress saturated steam into saturated liquid (process d-a) (in the Rankine cycle the pump simply raises the pressure of saturated liquid to the boiler pressure). There is also the problem of the output of the turbine involving steam that may be too wet causing blade corrosion (process b-c) (the Rankine cycle can use superheat steam that exits the turbine with dryer steam).

But probably the biggest limitation of all potential Carnot cycle applications is that in order for the cycle to be reversible, it must be carried out extremely slowly. So while the cycle may be the most efficient in terms of work out per heat in, the rate of work output (power) would be very low.

As I recall someone said you might get better gas economy if you put a Carnot engine in your car, but pedestrians would be passing you by!

Hope this helps.

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The Carnot Process is an ideal process to gain Energy from a temperature difference. I'll describe a slightly simpler process, though the general idea should stay the same.

Say you have a gas filled cylinder with a piston. If the pressure rises, the piston moves, unless it's held in place by breaks.

This cylinder is now heated and cooled.

  1. First, heating it while holding the piston, the pressure rises.
  2. Before switching to cooling, the piston is released and the gas allowed to expand. Here is the point, where we could extract energy.
  3. While cooling, the piston is held in place again and the pressure drops.
  4. Before heating it again, we allow the piston to contract. (I.e. the ambient air pressure pushes the piston back in) Again, we could extract energy here.

The differences to the Carnot process are threefold:

  1. the piston wouldn't be fixed,but expand and contract "cleverly" while heated and cooled.
  2. it turns out if you invest back a bit of energy to compress the gas more than it wants to before heating up and expand it a bit further before cooling down, the efficiency increases.
  3. the Carnot cycle works as defined only if you have infinite time for expansion and contraction. In real engines, truncated Carnot cycles are used.

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